Some problems occurs when your Internet security program was set
to trust the previous version of Firefox, but no longer recognizes your
updated version as trusted. Now how to fix the problem: To allow
Firefox to connect to the Internet again;

Make sure your Internet security software is up-to-date (i.e. you are running the latest version)

Remove Firefox from your program's list of trusted or recognized programs, then add it back. For detailed instructions, see

Some problems occurs when your Internet security program was set
to trust the previous version of Firefox, but no longer recognizes your
updated version as trusted. Now how to fix the problem: To allow
Firefox to connect to the Internet again;
* Make sure your Internet security software is up-to-date (i.e. you are running the latest version)
* Remove Firefox from your program's list of trusted or recognized programs, then add it back. For detailed instructions, see
'''[https://support.mozilla.org/en-US/kb/configure-firewalls-so-firefox-can-access-internet Configure firewalls so that Firefox can access the Internet.]''' {web link}

Create a new profile as a test to check if your current profile is causing the problem.
See "Creating a profile":
*https://support.mozilla.org/kb/profile-manager-create-and-remove-firefox-profiles
*http://kb.mozillazine.org/Standard_diagnostic_-_Firefox#Profile_issues
If the new profile works then you can transfer files from a previously used profile to the new profile, but be cautious not to copy corrupted files to avoid carrying over problems.
*http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox
If you updated then try to (re)install the latest release.
Download a new copy of the Firefox application and save the disk image file to the desktop
*Firefox 31.0: https://www.mozilla.org/en-US/firefox/all.html
*Trash the current Firefox application (open the Applications folder in the Finder and drag the Firefox application to the Trash) to do a clean (re)install
*Install the new version that you have downloaded
*https://support.mozilla.org/kb/Installing+Firefox+on+Mac
Your personal data is stored elsewhere in the Firefox profile folder, so you won't lose your bookmarks and other personal data when you uninstall and (re)install Firefox.
*http://kb.mozillazine.org/Profile_folder_-_Firefox
Note that Firefox 32.0 will be released in a few days (next Tuesday)